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Georgian Mathematical Journal

Volume 9 (2002), Number 1, 197–

A SEMIMARTINGALE BELLMAN EQUATION AND THE

VARIANCE-OPTIMAL MARTINGALE MEASURE.

CORRECTION

M. MANIA AND R. TEVZADZE

Abstract. Corrections are given for [1], most of which consist in replacing “ess sup” by “ess inf ” in all the exposed formulas.

2000 Mathematics Subject Classification: 91B28, 60H30, 90C39.

Key words and phrases: Backward semimartingale equation, incomplete markets, contingent claim pricing, variance-optimal martingale measure, the Bellman equation.

Unfortunately, [1] contains some distortions of the meaning most of which

can be corrected as follows: replace throughout the paper “ess sup” by “ess inf”

in all the exposed formulas; delete the second summand of

µ

(

t, x

) in the third

line of formula (4.17).

References

1. M. Mania and R. Tevzadze, A semimartingale Bellman equation and the variance-optimal martingale measure.Georgian Math. J.7(2000), No. 4. 765–792.

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